P and Q completed a work together and were paid rs 1,080 and rs. 1,440, respectively. If P can do the entire work in 20 days, how many days did they take to complete the work together?

Efficiency=Money paid

P/Q = 1080/1440=3/4
Total work = 3*20=60
(As efficiency of P is 3 and can do the work in 20days)
P+Q will do the work in 60/3+4=60/7= 8 4/7 days.

Sorry dear, @ oobleck, i didn't understand 3/4 concept

Well, P and Q make quite the dynamic duo, don't they? Let's crunch some numbers and solve this puzzle.

We know that P can complete the entire work in 20 days. So if they worked together for 20 days, P would have done all the work. In that case, P would have been paid the full amount of Rs.1,080.

But our friend Q also deserves a slice of the pie. He was paid Rs.1,440, which is more than P. This means that Q worked for more than 20 days.

To find out how many days they took together, we need to figure out the difference in the amount they were paid. So, the difference between Rs.1,440 and Rs.1,080 is Rs.360.

Now, we know that Q's extra work (Rs.360) is equal to what P can do in 20 days. This means that Q's additional work took him 20 days.

So, together, P and Q completed the entire work in 20 days plus Q's extra 20 days, which gives us a grand total of 40 days.

In conclusion, P and Q took 40 days to complete the work together. They may not be the fastest workers, but hey, slow and steady wins the race, right?

To solve this problem, we need to determine how much work P and Q can individually complete per day and then calculate the number of days it takes for them to complete the work together.

Let's start by finding out how much work P can complete in a day. We are given that P can complete the entire work in 20 days. Therefore, in one day, P completes 1/20th of the work.

Next, we need to calculate how much work Q can complete in a day. We are given that Q was paid Rs. 1,440 for completing the work. We know that payment is proportional to the amount of work completed. Since P was paid Rs. 1,080 for completing the work, we can write the following proportion:

P's work / Q's work = P's payment / Q's payment

1/20 / Q's work = 1,080 / 1,440

Simplifying the equation, we have:

1/20Q = 3/4

To solve for Q's work, we can cross-multiply:

1 * 4 = 20 * 3Q

4 = 60Q

Q = 4/60 = 1/15

Therefore, Q can complete 1/15th of the work in one day.

Now, we can calculate how many days it takes for P and Q to complete the work together. In one day, their combined work is:

1/20 + 1/15 = 3/60 + 4/60 = 7/60

This means that P and Q together complete 7/60th of the work in one day.

To find the number of days it takes for them to complete the entire work together, we can create the following equation:

(7/60) * Number of days = 1

Simplifying the equation, we have:

Number of days = 60/7

Therefore, they take approximately 8.57 days (or rounding off to the nearest whole number, 9 days) to complete the work together.

How 3/4 came??

Kindly explain @oobleck

he got paid 3/4 as much, so ...

no way to tell. How is their pay related to the time worked?

If their hourly pay rate is the same, then it appears that P worked 3/4 as long as Q.
So if P can do the job in 20 days, Q can do it in 80/3 days.
1/20 + 1/(80/3) = 7/80
So they can do the job in 80/7 days together